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Simplifying 2x * 2x + -3x = 14 Reorder the terms for easier multiplication: 2 * 2x * x + -3x = 14 Multiply 2 * 2 4x * x + -3x = 14 Multiply x * x 4x2 + -3x = 14 Reorder the terms: -3x + 4x2 = 14 Solving -3x + 4x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + -3x + 4x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.75x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.75x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.75x + x2 = 0 + 3.5 -0.75x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.75x + x2 = 3.5 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 3.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 3.5 + 0.140625 Combine like terms: 3.5 + 0.140625 = 3.640625 0.140625 + -0.75x + x2 = 3.640625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 3.640625 Calculate the square root of the right side: 1.90804219 Break this problem into two subproblems by setting (x + -0.375) equal to 1.90804219 and -1.90804219.Subproblem 1
x + -0.375 = 1.90804219 Simplifying x + -0.375 = 1.90804219 Reorder the terms: -0.375 + x = 1.90804219 Solving -0.375 + x = 1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.90804219 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.90804219 + 0.375 x = 1.90804219 + 0.375 Combine like terms: 1.90804219 + 0.375 = 2.28304219 x = 2.28304219 Simplifying x = 2.28304219Subproblem 2
x + -0.375 = -1.90804219 Simplifying x + -0.375 = -1.90804219 Reorder the terms: -0.375 + x = -1.90804219 Solving -0.375 + x = -1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.90804219 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.90804219 + 0.375 x = -1.90804219 + 0.375 Combine like terms: -1.90804219 + 0.375 = -1.53304219 x = -1.53304219 Simplifying x = -1.53304219Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.28304219, -1.53304219}
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